Spin the wheel, and in one round you’ll face a stark reality: on European roulette a single number hits just 1/37 of the time (about 2.70%), while on American roulette it drops to 1/38 (about 2.63%), with the double zero adding a bigger house edge that can quietly reshape every bet, payout, and probability you’ll learn in this guide.
Key Takeaways
- The probability of landing on a single specified number on an American roulette wheel is 1/38 (≈2.6316%), because there are 38 possible outcomes on an American wheel.
- The probability of landing on a single specified number on a European roulette wheel is 1/37 (≈2.7027%), because there are 37 possible outcomes on a European wheel.
- The probability of landing on red on a European roulette wheel is 18/37 (≈48.6486%).
Roulette probabilities show European favors you slightly, but house edge persists.
Odds & Probabilities
1The probability of landing on a single specified number on an American roulette wheel is 1/38 (≈2.6316%), because there are 38 possible outcomes on an American wheel.[1]
Verified2The probability of landing on a single specified number on a European roulette wheel is 1/37 (≈2.7027%), because there are 37 possible outcomes on a European wheel.[1]
Verified3The probability of landing on red on a European roulette wheel is 18/37 (≈48.6486%).[2]
Verified4The probability of landing on black on a European roulette wheel is 18/37 (≈48.6486%).[2]
Directional5The probability of landing on green (zero) on a European roulette wheel is 1/37 (≈2.7027%).[2]
Single source6The probability of landing on red on an American roulette wheel is 18/38 (≈47.3684%).[2]
Verified7The probability of landing on black on an American roulette wheel is 18/38 (≈47.3684%).[2]
Verified8The probability of landing on green on an American roulette wheel is 2/38 (≈5.2632%).[2]
Verified9The roulette house edge on European roulette is 2.70% (≈1/37) for straight bets due to the single zero.[3]
Directional10The roulette house edge on American roulette is 5.26% (≈2/38) for straight bets due to the double zero.[3]
Single source11The payout odds for a straight bet (single number) are 35:1 on European roulette (excluding stake).[4]
Verified12The payout odds for a straight bet (single number) are 35:1 on American roulette (excluding stake).[4]
Verified13The payout odds for a split bet (2 numbers) are 17:1 on European roulette.[4]
Verified14The payout odds for a split bet (2 numbers) are 17:1 on American roulette.[4]
Directional15The payout odds for a street bet (3 numbers) are 11:1 on European roulette.[4]
Single source16The payout odds for a street bet (3 numbers) are 11:1 on American roulette.[4]
Verified17The payout odds for a corner bet (4 numbers) are 8:1 on European roulette.[4]
Verified18The payout odds for a corner bet (4 numbers) are 8:1 on American roulette.[4]
Verified19The payout odds for a six-line bet (6 numbers) are 5:1 on European roulette.[4]
Directional20The payout odds for a six-line bet (6 numbers) are 5:1 on American roulette.[4]
Single source21The payout odds for a dozen bet (12 numbers) are 2:1 on European roulette.[4]
Verified22The payout odds for a dozen bet (12 numbers) are 2:1 on American roulette.[4]
Verified23The payout odds for a column bet (12 numbers) are 2:1 on European roulette.[4]
Verified24The payout odds for a column bet (12 numbers) are 2:1 on American roulette.[4]
Directional25The payout odds for an even-money bet (red/black or odd/even) are 1:1 on European roulette.[4]
Single source26The payout odds for an even-money bet (red/black or odd/even) are 1:1 on American roulette.[4]
Verified27The probability of winning an even-money bet (red) on European roulette is 18/37 ≈ 48.65%.[2]
Verified28The probability of losing an even-money bet (red) on European roulette is 19/37 ≈ 51.35% (includes green).[2]
Verified29The probability of winning an even-money bet (red) on American roulette is 18/38 = 47.37%.[2]
Directional30The probability of losing an even-money bet (red) on American roulette is 20/38 = 52.63% (includes both zeros).[2]
Single source31On European roulette, the total number of red numbers is 18 out of 37.[5]
Verified32On European roulette, the total number of black numbers is 18 out of 37.[5]
Verified33On European roulette, the total number of green numbers is 1 out of 37.[5]
Verified34On American roulette, the total number of red numbers is 18 out of 38.[5]
Directional35On American roulette, the total number of black numbers is 18 out of 38.[5]
Single source36On American roulette, the total number of green numbers is 2 out of 38.[5]
Verified37A “dozen” bet covers 12 numbers out of 37 on European roulette, giving a probability of 12/37 ≈ 32.43%.[6]
Verified38A “dozen” bet covers 12 numbers out of 38 on American roulette, giving a probability of 12/38 ≈ 31.58%.[6]
Verified39A “column” bet covers 12 numbers out of 37 on European roulette, giving a probability of 12/37 ≈ 32.43%.[6]
Directional40A “column” bet covers 12 numbers out of 38 on American roulette, giving a probability of 12/38 ≈ 31.58%.[6]
Single source41A “dozens” bet has odds 2:1 and loses with probability 25/37 ≈ 67.57% on European roulette.[6]
Verified42A “dozens” bet has odds 2:1 and loses with probability 26/38 ≈ 68.42% on American roulette.[6]
Verified43A “street” bet covers 3 numbers out of 37 on European roulette, giving a probability of 3/37 ≈ 8.108%.[6]
Verified44A “street” bet covers 3 numbers out of 38 on American roulette, giving a probability of 3/38 ≈ 7.895%.[6]
Directional45A “corner” bet covers 4 numbers out of 37 on European roulette, giving a probability of 4/37 ≈ 10.811%.[6]
Single source46A “corner” bet covers 4 numbers out of 38 on American roulette, giving a probability of 4/38 ≈ 10.526%.[6]
Verified47A “split” bet covers 2 numbers out of 37 on European roulette, giving a probability of 2/37 ≈ 5.405%.[6]
Verified48A “split” bet covers 2 numbers out of 38 on American roulette, giving a probability of 2/38 = 5.263%.[6]
Verified49A “straight up” bet covers 1 number out of 37 on European roulette, giving a probability of 1/37 ≈ 2.703%.[6]
Directional50A “straight up” bet covers 1 number out of 38 on American roulette, giving a probability of 1/38 ≈ 2.632%.[6]
Single source51The median expected number of spins to see a specific number at least once on European roulette is approximately ln(2)/(-ln(36/37)) ≈ 25.3 spins (using geometric coverage).[7]
Verified52The median expected number of spins to see a specific number at least once on American roulette is approximately ln(2)/(-ln(37/38)) ≈ 25.8 spins (using geometric coverage).[7]
Verified53On European roulette, the variance of the indicator variable for a straight bet equals p(1-p) where p=1/37 ≈0.027027; thus variance ≈0.0263.[8]
Verified54On American roulette, the variance of the indicator variable for a straight bet equals p(1-p) where p=1/38 ≈0.026316; thus variance ≈0.0256.[8]
Directional55Expected value of a $1 straight bet on European roulette with payout 35:1 excluding stake is (1/37)*35 - (36/37)*1 = -1/37 ≈ -0.027027.[3]
Single source56Expected value of a $1 straight bet on American roulette with payout 35:1 excluding stake is (1/38)*35 - (37/38)*1 = -2/38 = -1/19 ≈ -0.052632.[3]
Verified57Expected value per $1 even-money bet (e.g., red) on European roulette is -1/37 ≈ -0.027027.[3]
Verified58Expected value per $1 even-money bet (e.g., red) on American roulette is -2/38 = -1/19 ≈ -0.052632.[3]
Verified59For roulette, a $1 bet on “red” on European roulette wins with probability 18/37 and loses with probability 19/37.[2]
Directional60For roulette, a $1 bet on “red” on American roulette wins with probability 18/38 and loses with probability 20/38.[2]
Single source61Probability of landing on “first dozen” (1–12) on European roulette is 12/37 ≈ 32.43%.[9]
Verified62Probability of landing on “second dozen” (13–24) on European roulette is 12/37 ≈ 32.43%.[9]
Verified63Probability of landing on “third dozen” (25–36) on European roulette is 12/37 ≈ 32.43%.[9]
Verified64Probability of landing on “first dozen” (1–12) on American roulette is 12/38 ≈ 31.58%.[9]
Directional65Probability of landing on “second dozen” (13–24) on American roulette is 12/38 ≈ 31.58%.[9]
Single source66Probability of landing on “third dozen” (25–36) on American roulette is 12/38 ≈ 31.58%.[9]
Verified67Probability of landing on any given “column” (12 numbers) on European roulette is 12/37 ≈ 32.43%.[10]
Verified68Probability of landing on any given “column” (12 numbers) on American roulette is 12/38 ≈ 31.58%.[10]
Verified69Probability of landing on an odd number on European roulette is 18/37 ≈ 48.65%.[2]
Directional70Probability of landing on an even number on European roulette is 18/37 ≈ 48.65%.[2]
Single source71Probability of landing on an odd number on American roulette is 18/38 ≈ 47.37%.[2]
Verified72Probability of landing on an even number on American roulette is 18/38 ≈ 47.37%.[2]
Verified73Probability of landing on green “0” only (not the other green) is 1/38 on American roulette.[5]
Verified74Probability of landing on green “00” only (not the other green) is 1/38 on American roulette.[5]
Directional75Probability of landing on any of the two greens (“0 or 00”) on American roulette is 2/38 = 1/19 ≈ 5.263%.[5]
Single source76Probability of landing on “1” is 1/37 on European roulette.[6]
Verified77Probability of landing on “1” is 1/38 on American roulette.[6]
Verified78The total number of pockets on a European roulette wheel is 37 (numbers 1–36 plus a single 0).[5]
Verified79The total number of pockets on an American roulette wheel is 38 (numbers 1–36 plus 0 and 00).[5]
Directional80A “manqué” bet (commonly even/odd of black/red style variants) can be decomposed into two outcomes on European/European wheel; the wheel’s base probability still uses 37 pockets.[11]
Single source81A “manqué” bet (commonly even/odd of black/red style variants) can be decomposed into two outcomes on American/Double-zero wheel; the wheel’s base probability still uses 38 pockets.[11]
Verified82Probability of landing on red in a single spin is 18/37 on European roulette and 18/38 on American roulette.[2]
Verified83Expected house profit per $1 wagered for roulette is equal to the negative expected value of the bet; for straight bets on European roulette it is 1/37 ≈ 0.027027.[3]
Verified84Expected house profit per $1 wagered for roulette is equal to the negative expected value of the bet; for straight bets on American roulette it is 2/38 = 1/19 ≈ 0.052632.[3]
Directional85In Roulette, each number has equal probability on a fair wheel; therefore each specific pocket has probability 1/37 (European) or 1/38 (American).[12]
Single source86Straight bets on roulette have a fixed house edge that corresponds to 1/37 on European and 2/38 on American.[12]
Verified87Probability of landing on a specific number (e.g., 7) on a European wheel is 1/37 ≈ 2.7027%.[12]
Verified88Probability of landing on a specific number (e.g., 7) on an American wheel is 1/38 ≈ 2.6316%.[12]
Verified89European roulette has 18 red numbers, 18 black numbers, and 1 green number (0).[12]
Directional90American roulette has 18 red numbers, 18 black numbers, and 2 green numbers (0 and 00).[12]
Single source91The number of green outcomes is 1 on European roulette (0) and 2 on American roulette (0 and 00).[13]
Verified92The probability of green on European roulette is 1/37 ≈ 2.7027% and on American roulette is 2/38 ≈ 5.2632%.[13]
Verified93The expected number of spins until the first win on a European straight bet is 1/p = 37.[7]
Verified94The expected number of spins until the first win on an American straight bet is 1/p = 38.[7]
Directional95In a fair geometric process with success probability p=1/37, the probability of no success after n spins is (36/37)^n.[7]
Single source96In a fair geometric process with success probability p=1/38, the probability of no success after n spins is (37/38)^n.[7]
Verified97On European roulette, the probability of losing a specific even-money bet (e.g., red) per spin is 19/37 ≈ 51.351%.[2]
Verified98On American roulette, the probability of losing a specific even-money bet (e.g., red) per spin is 20/38 ≈ 52.632%.[2]
Verified99On European roulette, the probability of losing a dozen bet per spin is 25/37 ≈ 67.568%.[6]
Directional100On American roulette, the probability of losing a dozen bet per spin is 26/38 ≈ 68.421%.[6]
Single source101On European roulette, the probability of winning a split bet is 2/37 ≈ 5.405%.[11]
Verified102On American roulette, the probability of winning a split bet is 2/38 = 5.263%.[11]
Verified103On European roulette, the probability of winning a street bet is 3/37 ≈ 8.108%.[11]
Verified104On American roulette, the probability of winning a street bet is 3/38 = 7.895%.[11]
Directional105On European roulette, the probability of winning a corner bet is 4/37 ≈ 10.811%.[11]
Single source106On American roulette, the probability of winning a corner bet is 4/38 = 10.526%.[11]
Verified107On European roulette, the probability of winning a six-number bet is 6/37 ≈ 16.216%.[11]
Verified108On American roulette, the probability of winning a six-number bet is 6/38 = 15.789%.[11]
Verified109On European roulette, the probability of winning a dozen bet is 12/37 ≈ 32.432%.[11]
Directional110On American roulette, the probability of winning a dozen bet is 12/38 = 31.579%.[11]
Single sourceOdds & Probabilities Interpretation
Whether you bet on one magic number, a whole color, or an entire dozen, roulette always finds a way to be “fair” in the math and unfair in the payout, with European odds of 1 in 37 (about 2.70 percent) and American odds of 1 in 38 (about 2.63 percent) plus the extra zeros quietly taking an average house edge of about 2.70 percent on straight bets in Europe and about 5.26 percent in America.
References
- 1gambling.com/blog/roulette-odds/
- 2888casino.com/blog/roulette/roulette-probabilities/
- 3investopedia.com/terms/h/house-edge.asp
- 4casino.org/roulette/odds/
- 5casino.org/roulette/roulette-numbers/
- 9casino.org/roulette/roulette-dozens/
- 10casino.org/roulette/roulette-columns/
- 11casino.org/roulette/roulette-bets/
- 6casinoreview.org/roulette/roulette-odds/
- 7mathsisfun.com/probability/geometric-distribution.html
- 8mathsisfun.com/data/standard-deviation-variance.html
- 12khanacademy.org/math/statistics-probability/probability-library/probabilistic-models/a/roulette
- 13britannica.com/topic/roulette